What do the following two equations represent? $-5x-4y = 4$ $-5x-4y = 0$
Solution: Putting the first equation in $y = mx + b$ form gives: $-5x-4y = 4$ $-4y = 5x+4$ $y = -\dfrac{5}{4}x - 1$ Putting the second equation in $y = mx + b$ form gives: $-5x-4y = 0$ $-4y = 5x$ $y = -\dfrac{5}{4}x + 0$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.